Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #3165 |
380 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=e,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^10,d^c=dg142 conjugacy classes — view the full character table.
| maximal subgroup of | #14805878, #14805880, #14805882, … |
| maximal normal subgroup of | #14805878, #14805880, #14805882, … |
| maximal quotient of | #14754198, #14757159, #14757161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15054);